I decided to write a program that takes Doug's move usage statistics of Pokemon and converts them to a typical moveset used by that Pokemon during September.
Before I unveil the movesets, first I must explain how this program works.
Suppose Move 1 is used with probability p1 and Move 2 is used with probability p2. Without loss of generality, let's assume p1>p2. What is the probability that p1 and p2 are in the same moveset? This doesn't have an exact answer, unfortunately, but it does have a maximum and a minimum.
The maximum probability that both Moves 1 and 2 are in the same moveset is p2. This will happen if every moveset containing Move 2 also happens to contain Move 1.
The minimum probability is a bit more difficult to calculate. Suppose, as an example, that p1 = 70% and p2 = 40%. The worst case one can get is that 70% of the movesets have Move 1 and all the remaining 30% of the movesets have Move 2. However, since 40% of the movesets have Move 2, and not 30%, the remaining 10% must be in movesets among the 70% that have Move 1. Thus we see that the minimum probability that Moves 1 and 2 are together in the same moveset would be 10% in this case. We found this probability by calculating 70% + 40% - 100% = 10%.
It might happen that p1 and p2 don't sum up to a number greater than 100%. In that case, the minimum probability that Moves 1 and 2 are together would be 0, which means that it might happen that they never occur together in the same moveset.
So, to summarise:
Notice that if p1+p2 is greater than 1, we have a guarantee that at least one moveset contained Moves 1 and 2 together.
Using a similar argument, we can find the maximum and minimum probabilities for three moves to be together in the same moveset:
and also those for four moves:
Again, this implies that if p1+p2+p3+p4 is greater than 3, then we have a guarantee that at least one player used a moveset containing Moves 1, 2, 3 and 4.
The program would thus simply search for the minimum number of moves whose sum of their probabilities of being in a moveset exceeds 3. This minimum number might not be four. If it is not four (say, it is six), then it means that a moveset containing 4 of these 6 moves is certain to have been used by a player.
Let's illustrate this idea by creating a typical moveset for Abomasnow used in the Standard ladder:
Doug's statistics conveniently sorts the usage of moves in descending order. So we start with Blizzard, having a 76.2% chance of being in a moveset. The most used move is automatically written to be the first move in the typical moveset:
Next, we have Leech Seed with 68%. Summing 76.2% with 68%, we get 144.2%. Since this exceeds 100%, it means that there must exist a player having used an Abomasnow having Blizzard and Leech Seed in his or her moveset. Thus, we have, so far:
Next we have Substitute, whe 53.7% of usage. 53.7% + 144.2% = 197.9%. Argh... we're just short of 200%. This means that we don't have a guarantee that an Abomasnow moveset contained Blizzard, Leech Seed and Substitute in the same moveset. Hence, we go to the next move, Focus Punch, with 35%. 35% + 197.9% = 232.9%. This time we surpass the 200% mark. This means that we have a guarantee that three of the four moves Blizzard, Leech Seed, Substitute and Focus Punch are among the first three moves of a typical Abomasnow moveset. We can write this as:
We now continue. Wood Hammer has 33% of usage. 232.9% + 33% = 265.9%... still a long way to go to exceed 300%. So we continue with Protect, having 27.6% probability. 265.9% + 27.6% = 293.5%... again not quite 300%. Finally, Ice Shard has probability 23.4%. 293.5% + 23.4% = 316.9%, exceeding 300%. So we now have a guarantee that a typical Abomasnow moveset consists of four moves out of Blizzard, Leech Seed, Substitute, Focus Punch, Wood Hammer, Protect and Ice Shard. We can write this down as
That's all there is to it!
So here are the typical movesets of all Pokemon used in September, in the Standard, UU, Uber and Suspect ladders. There are also sorted in order of usage for your convenience. If you want to search for a Pokemon, hit Ctrl-F as usual.
Typical Movesets in Standard Ladder
Typical Movesets in UnderUsed Ladder
Typical Movesets in Uber Ladder
Typical Movesets in Suspect Ladder
As Doug likes to say, "happy stat hunting!" :)
Before I unveil the movesets, first I must explain how this program works.
Suppose Move 1 is used with probability p1 and Move 2 is used with probability p2. Without loss of generality, let's assume p1>p2. What is the probability that p1 and p2 are in the same moveset? This doesn't have an exact answer, unfortunately, but it does have a maximum and a minimum.
The maximum probability that both Moves 1 and 2 are in the same moveset is p2. This will happen if every moveset containing Move 2 also happens to contain Move 1.
The minimum probability is a bit more difficult to calculate. Suppose, as an example, that p1 = 70% and p2 = 40%. The worst case one can get is that 70% of the movesets have Move 1 and all the remaining 30% of the movesets have Move 2. However, since 40% of the movesets have Move 2, and not 30%, the remaining 10% must be in movesets among the 70% that have Move 1. Thus we see that the minimum probability that Moves 1 and 2 are together in the same moveset would be 10% in this case. We found this probability by calculating 70% + 40% - 100% = 10%.
It might happen that p1 and p2 don't sum up to a number greater than 100%. In that case, the minimum probability that Moves 1 and 2 are together would be 0, which means that it might happen that they never occur together in the same moveset.
So, to summarise:
Code:
Maximum probability that two moves are together in the same moveset = min(p1,p2)
Minimum probability that two moves are together in the same moveset = max(p1+p2-1,0)
where p1 and p2 are the probabilities that Moves 1 and 2 are in a moveset respectively.Using a similar argument, we can find the maximum and minimum probabilities for three moves to be together in the same moveset:
Code:
Maximum probability that three moves are together in the same moveset = min(p1,p2,p3)
Minimum probability that three moves are together in the same moveset = max(p1+p2+p3-2,0)
where pn is the probability that Move n is in a moveset.
Code:
Maximum probability that four moves are together in the same moveset = min(p1,p2,p3,p4)
Minimum probability that four moves are together in the same moveset = max(p1+p2+p3+p4-3,0)
where pn is the probability that Move n is in a moveset.The program would thus simply search for the minimum number of moves whose sum of their probabilities of being in a moveset exceeds 3. This minimum number might not be four. If it is not four (say, it is six), then it means that a moveset containing 4 of these 6 moves is certain to have been used by a player.
Let's illustrate this idea by creating a typical moveset for Abomasnow used in the Standard ladder:
Code:
| Abomasnow | Move | Blizzard | 76.2 |
| Abomasnow | Move | Leech Seed | 68.0 |
| Abomasnow | Move | Substitute | 53.7 |
| Abomasnow | Move | Focus Punch | 35.0 |
| Abomasnow | Move | Wood Hammer | 33.0 |
| Abomasnow | Move | Protect | 27.6 |
| Abomasnow | Move | Ice Shard | 23.4 |
| Abomasnow | Move | Earthquake | 16.0 |
| Abomasnow | Move | Grass Knot | 12.4 |
| Abomasnow | Move | Seed Bomb | 8.6 |
| Abomasnow | Move | Swords Dance | 7.6 |
| Abomasnow | Move | Energy Ball | 7.5 |
| Abomasnow | Move | Other (9) | < 6.8 |
Code:
- Blizzard
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Code:
- Blizzard
- Leech Seed
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Code:
- Blizzard
- Leech Seed
- Substitute
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Comments:
* Focus Punch can replace any of the first three moves listed.
Code:
- Blizzard
- Leech Seed
- Substitute
- Wood Hammer
Comments:
* Focus Punch can replace any of the first three moves listed.
* Protect and Ice Shard can replace any of the four moves listed.So here are the typical movesets of all Pokemon used in September, in the Standard, UU, Uber and Suspect ladders. There are also sorted in order of usage for your convenience. If you want to search for a Pokemon, hit Ctrl-F as usual.
Typical Movesets in Standard Ladder
Typical Movesets in UnderUsed Ladder
Typical Movesets in Uber Ladder
Typical Movesets in Suspect Ladder
As Doug likes to say, "happy stat hunting!" :)
